Could someone explain the whole Item Crafting thing to me? I've had a look at a TF2 Wiki, but I'm still confused... Thanks!

Also, do you get items completely randomly, or is there a certain way of getting them (Other than the new shop)?

As you play TF2, you sometimes find random item drops. You can either use these on your characters or use them to craft[or trade].
It's mostly for getting the rare hats, which can be obtained by crafting 3 refined metals or 4 refined metals and a class token to increase your chances of getting a certain hat, but can also be used for weapons as well.
http://www.tf2items.com/crafting/blueprints.php
Look there, there's a ton of recipies to choose from, and that's pretty much all you need to know about crafting.

Theres two Methods to obtains Items on your own, by Random drop, or for some, completing achievement Milestones.

As for crafting. It allows you to make weapons or if you have the right materials, Hats.
But with the Trading system up, tons of people are trading items. So it's good to keep your eyes out.

Full Article on Crafting : Here